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How to represent a tree in a map?

How to represent and visualize a lot of information at a glance is a hot topic in IT.
A Treemap, also known as Heatmap, is an important tool for this. A TreeMap graphically represents a hierarchical structure.
Typically, the hierarchy will involve a tree of nodes of different sizes and different colours.

A Heatmap/Treemap is great to see a lot of information in one glance. It can be interactive and allow you to drill down into some section of the hierarchy. More on treemapping on Wikipedia.

Each box on the chart may be contained in another box (e.g. Microsoft and Sun in the Technology box, CitiGroup in Banking, etc hence the hierachical view.

The size is usually determined by the relative size of a parameter in comparison to the full size of the chart (i.e. the 'bigger' X, the bigger it is on the chart).

The colour shows another dimension in the parameters, like a movement in time (i.e. conventionally the greener, the bigger the increase; the 'redder', the bigger the decrease!).

A tree structure may includes more or less important elements.
For example, in a tree structure of files, there can be big files or small files.
It can be then interesting to know which directory is the biggest on a hard disk, at a glance!.
But, in a treeview, we can't distinguish the significant elements.
Treemap makes it possible to represent each element in a rectangle of more or less big size
according to its importance in the tree structure.
Moreover, we can add a code color which makes it possible to introduce new information into the representation of the tree structure.

For example, you can use Treemap to see :

which is the most important directory on your hard disk.

if your portfolio of stocks is well distributed between the various industry sectors.